Sok Li Lim

A direct procedure for monitoring the coefficient of variation using a variable sample size scheme

ABSTRACT A variable sample size (VSS) scheme directly monitoring the coefficient of variation (CV), instead of monitoring the transformed statistics, is proposed. Optimal chart parameters are computed based on two criteria: (i) minimizing the out-of-control ARL (ARL1) and (ii) minimizing the out-of-control ASS (ASS1). Then the performances are compared between these two criteria. The advantages of the proposed chart over the VSS chart based on the transformed statistics in the existing literature are: the former (i) provides an easier alternative as no transformation is involved and (ii) requires less number of observations to detect a shift when ASS1 is minimized.

Economic and economic-statistical designs of the side sensitive group runs chart

A new optimization algorithm is proposed for the economic models of the SSGR chart.Optimal design parameters of the SSGR chart are computed based on ARL and EARL.Sensitivity analyses are conducted for various input parameters of the cost model.Effects of misspecification of the shift size on the performance of the SSGR chart are investigated.The performance of the SSGR chart is compared with that of the Shewhart X ? , synthetic, GR and EWMA charts. The idea of proposing the economic and economic-statistical designs of the side sensitive group runs (SSGR) chart is presented in this paper. In the economic design, a simplified algorithm is used to search for the optimal design parameters that minimize the expected hourly cost. Nevertheless, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, in order to improve the effectiveness of the control chart in detecting process shifts, the economic-statistical design takes into account the statistical properties while the cost is minimized by placing statistical constraints upon the cost model of the economic design. Besides formulating the economic and economic-statistical designs based on the average run length (ARL), the economic and economic-statistical designs of the SSGR chart are also formulated based on the expected average run length (EARL) since the process shift size is usually unknown in real situations. In this paper, the sensitivity analyses of the optimal cost and the optimal design parameters are implemented for various input parameters. The effects of misspecification of the shift size on the performance of the SSGR chart are also illustrated based on numerical examples for different input parameters. This paper will also look at whether the SSGR chart performs economically better than the Shewhart X ? , synthetic, group runs (GR) and EWMA charts in the economic-statistical design based on the EARL. From the results of comparison, it is shown that the economic performance of the SSGR chart is better than that of the other four control charts in most practical situations.

The economic and economic-statistical designs of the Hotelling's T2 chart based on the expected average run length

ABSTRACT Existing economic and economic-statistical designs require practitioners to specify the Mahalanobis Distance Shift Size (MDSS) as an exact value. However, practitioners may find it difficult to specify this distance. This article proposes the economic and economic-statistical designs of the Hotellings T2 chart, where practitioners do not have to specify the MDSS. Adopting optimal design parameters based on the wrong MDSS results in a significant increase in cost. In comparison, adopting the optimal design parameters based on the proposed methodology results in a slight increase in cost. This article also studies the effects of different input parameters and statistical constraints.

Monitoring the coefficient of variation using a variable parameters chart

ABSTRACT This article is the first of its kind which proposes a Variable Parameters (VP) chart to monitor the coefficient of variation (CV). Formulae for various performance measures and the algorithms to optimize these performance measures are proposed. The VP CV chart consistently outperforms the five alternative CV charts in the literature, for all shift sizes. Compared to the Exponentially Weighted Moving Average (EWMA) CV2 chart, the VP CV chart outperforms it for moderate and large shift sizes, while for small shift sizes, the EWMA CV2 chart outperforms the VP CV chart. Subsequently, the VP CV chart is implemented on an industrial example.

A Cost Comparison of the Synthetic and Shewhart X Charts

Although control charts are useful tools for quality monitoring, the cost of implementing the chart may prohibit practitioners from implementing it. The cost of sampling, cost of repairs, cost of defective products due to a failure in detecting out-of-control conditions, cost of false alarms etc can be prohibitively high. Hence, this paper compares the cost between the synthetic X and Shewhart X charts, so that practitioners could identify which chart is more economical to implement. The synthetic X chart was initially proposed to improve the ability in detecting changes in the process mean. This paper has shown that not only does the synthetic X chart has better detection ability than the Shewhart X chart, it is also more economical to implement. Thus, practitioners are recommended to adopt the synthetic X chart.

Monitoring the coefficient of variation using a variable sample size EWMA chart

Abstract Control charts for monitoring the coefficient of variation (CV) have been receiving a lot of attention in the literature, with numerous more powerful and robust CV charts being proposed. CV charts are attracting attention due to their usefulness in monitoring processes with an inconsistent mean and a standard deviation which changes with the mean. These processes could not be monitored by conventional mean and/or standard deviation-type charts. One of the strategies to improve the performance of CV charts is by incorporating adaptive features, i.e. by varying the chart’s parameters according to past sample information. Hence, this paper proposes a variable sample size (VSS) Exponentially Weighted Moving Average (EWMA) chart to monitor the CV squared ( γ 2 ) , which is not available in the literature. The proposed chart allows different sample sizes to be adopted in the EWMA chart according to prior sample information. This paper shows the derivation of formulae to compute the average run length (ARL), average sample size (ASS) and expected average run length (EARL). Subsequently, an optimization algorithm to optimize the performance of the proposed chart is developed. Tables of optimal charting parameters are also provided. Next, the performance of the proposed chart is compared with five existing CV charts in the literature. The comparison shows that the proposed chart outperforms the five existing CV charts in almost all scenarios. Finally, this paper shows the implementation of the VSS EWMA- γ 2 chart on an actual industrial example.

Optimal design of the modified group runs (MGR) chart when process parameters are estimated

Abstract The performance of variable charts is commonly investigated based on the assumption of known process parameters. However, the process parameters are usually unknown and have to be estimated from a limited number of Phase-I samples, leading to a deterioration of a control chart’s performance. To overcome this problem, we examine the performance of the modified group runs (MGR) chart with estimated process parameters. A table containing the optimal parameters of the proposed chart when the process parameters are estimated is also given. These optimal parameters will enable practitioners to obtain a similar in-control performance as the known process parameters case.

The coefficient of variation chart with measurement error

Abstract This paper proposes one-sided coefficient of variation (CV) charts with a linearly covariate error model. The one-sided CV charts are the downward and upward CV charts, which detect decreasing and increasing shifts, respectively. Ignoring the presence of measurement error leads to erroneous conclusions regarding the average run length, especially for small number of measurements per item. However, when measurement error is not ignored in computing the control limits, the performance between the CV charts with and without measurement error is similar. It is recommended to adopt the methods proposed in this paper as a general procedure since in the absence of measurement error, the control limits can be set by letting the size of the measurement error to be zero, whereas traditional methods which assume no measurement error will result in dubious results in the presence of measurement error. Finally, the proposed chart is applied on an illustrative example.

Effects of misspecification of the loss function on the economic-statistical design of the synthetic X̄ chart

The optimal choice of design parameters has a huge impact on a control charts performance. The economic-statistical design balances the economic and statistical performance of a chart, by selecting design parameters which minimize the cost subjected to statistical constraints. To compute the quality loss as a result of deviations from the target value, quality loss functions are often used. However, practitioners may incorrectly choose the wrong type of loss function to describe the quality loss. This paper studies the effects when the type of loss function is misspecified. This study is done on the synthetic X̅ chart. We focus our attention on the linear, quadratic and exponential loss functions.